Nonexistence of a crepant resolution of some moduli spaces of sheaves on a K3 surface

2004/07/07 by Jaeyoo Choy, Choy, Jaeyoo, Young-Hoon Kiem +1
Mathematics · #53D30 (Primary) 14J60 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J60 #msc:53D30

paper · pdf · doi:10.48550/arxiv.math/0407100

18 pages

arxiv created 2005/04/10 · arxiv updated 2009/12/01

Abstract

Let M_c=M(2,0,c) be the moduli space of O(1)-semistable rank 2 torsion-free sheaves with Chern classes c₁=0 and c₂=c on a K3 surface X where O(1) is a generic ample line bundle on X. When c=2n≥4 is even, M_c is a singular projective variety equipped with a symplectic structure on the smooth locus. In this paper, we show that there is no crepant resolution of M_2n for n≥ 3. This implies that there is no symplectic desingularization.

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